A natural form for large amplitude time-periodic acoustic travelling waves in piezoelectric semiconductors

Abstract

The propagation of time-periodic acoustic waves in piezoelectric semiconductors is treated in the limit of weak electromechanical coupling. The perturbed acoustic mode of the linear regime is shown to have a natural extension into the nonlinear regime which is defined uniquely without introducing ad hoc boundary conditions. The properties of this natural solution are investigated by means of a perturbation expansion in powers of the fundamental amplitude. When the average electron drift velocity is just above the velocity of sound, the nonlinear gain at all frequencies is intermediate between the two values obtained from the linear gain formula by inserting the drift velocity and the dc field times the mobility.